### Abstract

Local coordinates based on the Voronoi diagram are
used in natural neighbour interpolation to quantify
the "neighbourliness" of data sites. In this paper, we
propose a generalisation of the local coordinates and
natural neighbour interpolation based on the ordinary
Voronoi diagram, to the Voronoi diagram for a set
of points and oriented line segments in the Euclidean
plane. This generalisation allows one to model linear
discontinuities that are not modelable through current
interpolation techniques. We present the application
of the natural neighbour interpolation based on these
local coordinates to digital terrain modelling. In our
case, the data sites can be either points or oriented line
segments. We use this natural neighbour interpolation
in order to interpolate elevations from the neighbouring data sites, and construct a digital terrain model.
We show an example of use of this extended interpolation technique for the modelling of linear vertical faults,
dams or bridges.

Original language | English |
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Title of host publication | Proceedings of the 13th Canadian Conference on Computational Geometry (CCCG'01) |

Publication date | 2001 |

Pages | 29-32 |

Publication status | Published - 2001 |

Externally published | Yes |

Event | 13th Canadian Conference on Computational Geometry - Waterloo, Canada Duration: 13 Aug 2001 → 15 Aug 2001 Conference number: 13 http://www.cccg.ca/proceedings/2001/ |

### Conference

Conference | 13th Canadian Conference on Computational Geometry |
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Number | 13 |

Country | Canada |

City | Waterloo |

Period | 13/08/2001 → 15/08/2001 |

Internet address |

## Cite this

Antón Castro, FF., Mioc, D., & Gold, C. M. (2001). Line Voronoi diagram based interpolation and application to digital terrain modelling. In

*Proceedings of the 13th Canadian Conference on Computational Geometry (CCCG'01)*(pp. 29-32)